Probably of imitative origin.
chumble (third-person singular simple present chumbles, present participle chumbling, simple past and past participle chumbled)
- To peck at or nibble.
- 1964: Little dogs (his spaniel’s eyes encountered many) leaped and fawned about her, their sharp neat teeth clogging in the soft candy they chumbled from her gloved hand. — Anthony Burgess, Nothing Like The Sun